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Fungrim entry: b9c50f

φ ⁣(n)=npn(11p)\varphi\!\left(n\right) = n \prod_{p \mid n} \left(1 - \frac{1}{p}\right)
Assumptions:nZ1n \in \mathbb{Z}_{\ge 1}
TeX:
\varphi\!\left(n\right) = n \prod_{p \mid n} \left(1 - \frac{1}{p}\right)

n \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
Totientφ ⁣(n)\varphi\!\left(n\right) Euler totient function
PrimeProductpf ⁣(p)\prod_{p} f\!\left(p\right) Product over primes
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("b9c50f"),
    Formula(Equal(Totient(n), Mul(n, PrimeProduct(Parentheses(Sub(1, Div(1, p))), p, Divides(p, n))))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(1))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-08-17 11:32:46.829430 UTC